Universal finite-size effects in the rate of growth processes

Abstract

Kinetic roughening of the growing surface generates universal finite-size corrections in the growth rate of films and crystals. For thin films the correction scales with the film thickness h as h- alpha perpendicular to ; for thick films it scales with the substrate size L as L- alpha //, where a/sub ///=2(1- zeta ) and alpha perpendicular to =2(1- zeta )/z in terms of the kinetic roughening exponents zeta and z. For ballistic deposits this implies a similar correction in the density. The coefficient of the correction is proportional to the KPZ coupling constant lambda . For one-dimensional substrates alpha /sub ///=1 and alpha perpendicular to =2/3. These predictions are corroborated by computer simulations of growth and deposition on one- and two-dimensional substrates, and by exact results for one-dimensional models. Different exponents apply in the weak results for one-dimensional models. Different exponents apply in the weak coupling regime and at kinetic roughening transitions.